value of integration , Mathematics

Assignment Help:

what is the value of integration limit n-> infinity [n!/n to the power n]to the power 1/n

Solution)  limit n-->inf.    [1 + (n!-n^n)/n^n]^1/n

= e^ limit n-->inf.    {(n!-n^n)/n^n}.1/n         

                             (applying formula lim x-->a  [1 + f(x)]^g(x) =    e ^ {lim x-->a    f(x).g(x)}  )

=e ^ lim n-->inf.       (n-1)!/(n)^n-1   -   1/n

=e ^ lim n---> inf.     (1-1/n)(1-2/n)(1-3/n)......1/n   -    1/n

=e ^ (1-o)(1-0).....(1-0).0  -   0

=e ^ 0-0

=1

hence, integation 1= x + C

 

 


Related Discussions:- value of integration

Ordinary and partial differential equations, A differential equation is ter...

A differential equation is termed as an ordinary differential equation, abbreviated through odes, if this has ordinary derivatives in it. Similarly, a differential equation is term

Determine the height of the washington monument, Determine the height of th...

Determine the height of the Washington Monument to the nearest tenth of a meter. a. 157.8 m b. 169.3 m c. 170.1 m d. 192.2 m c. The height of the monument is the add

Algebra, find the value of A and B if the following polynomials are perfect...

find the value of A and B if the following polynomials are perfect square:

Yield volatility and graph, This question has two related parts, (a) and (b...

This question has two related parts, (a) and (b). (a) Use the daily yields in the table below to compute a daily standard deviation of yields. Next annualize the daily standard

Acid solution, A 90% acid solution is mixed with a 97% acid solution to obt...

A 90% acid solution is mixed with a 97% acid solution to obtain 21 litres of a 95% solution. Findout the quantity of every solutions to get the resultant mixture.

What is partially ordered set, What is Partially Ordered Set?  Let  S = {a,...

What is Partially Ordered Set?  Let  S = {a,b,c} and A = P(S). Draw the Hasse diagram of the poset A with the partial order ⊆ (set inclusion).   Ans: Let R be a relation define

Grouping-categories of situations requiring division , Grouping - situatio...

Grouping - situations in which we need to find the number of portions of a given size which can be obtained from a given quantity. (e.g., if there are 50 children in a class and t

Math, A small square is located inside a bigger square. The length of the s...

A small square is located inside a bigger square. The length of the small square is 3 in. The length of the large square is 7m. What is the area of the big square if you take out t

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd